Well, first up, the software situation is exactly the thing that they're trying to remedy at the moment (and coincidentally, that's also the main topic of this thread). Will they succeed? It's too early to tell, but the next generation is at least a couple of years away. I agree that right now Xbox faces an uphill battle when it comes to the power of the brand. By the end of the last generation they managed to achieve almost parity with PlayStation, but that was squandered away pretty quickly. However, the very success of Xbox 360 (which was neither significantly more nor significantly less powerful than PS3), together with the seesaw that Nintendo seem to be on with their systems, shows that those things are not set in stone.
Let's not presume that launching at the same time necessarily equals hardware parity. It does not, that could swing either way, based on the decisions made. One of them might even deliberately go for something more unique, like Nintendo so often does.
But if we do presume parity, then Sony certainly has an advantage in mind share, and an advantage in software. Microsoft, on the other hand, enjoys an advantage in services and pro-consumer policies (crossplay, Play Anywhere, mods, Game Preview, refunds, gifting, BC, EA Access, Game Pass and so on). If Microsoft decide to wait in order to be able to offer even better hardware, they might win on that front, but Sony will further improve their mind share, and their software situation (because PS5 will get a head start with third parties, just like Xbox 360 did in 2005). Nothing guarantees that Microsoft will win if they launch simultaneously with Sony - in fact, they might be in disadvantage overall - but I simply believe that their odds will further decrease if they decide to wait. Remember that hardware superiority guarantees nothing either, as Wii so clearly demonstrated last gen, and the importance of hardware might be even diminished in the future.
And you know, we're talking about "winning" and "losing", but it's not a clear-cut distinction, and there are multiple criteria. After all, platform holders primarily think about those things in terms of making money, and install base is just one thing that might help them achieve better results - a means to an end, not an end goal itself. A lot could change over the next few years - actually, things are bound to change, and they're changing already - and it's going to be interesting to observe.